Question

The ratio of magnetic potential due to magnetic dipole at the end to that at the broad side on a position for the same distance from it is :

• A. zero
• B. $\infty$
• C. 1
• D. 2

Answer 1

Answer: (B)

$\infty$

Magnetic potential(V) at any point due to bar magnet is given by
$V=\frac{{\mu }_{0}M\cos \theta }{4\pi r^2}$
where, variables have their usual meanings.

Magnetic potential due to magnetic dipole along axial line i.e. end on position,
$\theta =0\Rightarrow \cos \theta =1$
$\therefore V_a=\frac{{\mu }_{0}M}{4\pi r^2}$

And magnetic potential due to magnetic dipole along equatorial line i.e. on broad side,
$\theta ={90}^{\circ }\Rightarrow \cos \theta =0$
$\therefore V_e=0$

Hence the ratio, $\frac{Va}{Ve}=\infty$